So then I should have the same problem connecting the L7s to the base audio? (no sound coming from front speakers?)

Correct.

Only the stereo woofers are designed to pass the signal back to the vehicle wiring harness (parallel wiring) and into the front doors.

You could build an adapter (if this is all you plan on doing) but if you are redoing your system, the "right" answer is to properly crossover your signal from your amp to HP the doors and LP the woofers.